Is it Open Mike or Open Mic?
Answer: The correct spelling is "Open Mic"
Mic is the shortened form of microphone refering to the electric sound wand on stage that is openly available for use by anyone who turns up at such an event.
Mike — on the other hand — is an informal handle used when refering to someone named Michael. If the phrase was "Open Mike" it would mean "A man named Micheal who is openly available for use by anyone". If you are looking for that kind of thing and have arrived here by accident, may I suggest searching Facebook for people named Michael, but please keep the results of that little experiment to yourself.
Examples of famous Mikes
Musician with poetic British band The Streets
Comedian, actor and animation voice artist
Lead singer of Mike and the Mechanics